Measuring the Field of View for the iPhone 6 Camera

The angular field of view (often called FOV) is a measure of the angular size for an image produced by a camera. Different cameras have different FOV.

But who cares, right? I care. I care because it matters when you are using a camera to measure angles. Really, this all has to do with angular size. Let’s look at a bee in a sample image.

If I know the camera’s field of view, I can use this image to find the angular size of the bee. Once I have the angular size (I will call this θb), I can use the following relationship.

Just divide the length of the bee (L) by the distance from the bee to the camera (r) and you should get the angular size of the bee (in radians). Think about it. What if I took a whole bunch of bees and made them into a circle centered on the camera? In that case, the length of all of these bees would be the circumference of a circle (2πr). If I divide this by the distance (which is also r), I get an angular size of 2π. See it works. Ok, there is one small problem. If an object has a very large angular size, you don’t get the length of that object since different parts of the object will actually be different distances from the camera. Still, it works in most cases.

Now for an experimental method to determine the angular field of view for the iPhone 6. Why not just look this up? Two reasons. First, I don’t always trust camera specifications – especially when they aren’t so easy to find. Second, the experimental method is just fun.

Here is the plan. Look at several objects of a known size and known distance and make a graph (rather than just one object at one distance). I will take this presentation board and set it at different distances from camera.

If you want to do something like this yourself, here is a helpful tip. The tiles on the floor are usually standard sizes. In my office, they are 12 inches by 12 inches. I can just put the camera on one edge of a tile and count tiles for the distance. I will now record two things for each picture: the distance from the camera to object and the angular size of the object. But here is the thing – I don’t know the angular size. Instead, I will measure the ratio of the object’s angular size to the field of view for the camera. I will call this α such that:

Where s is the length of the object as a ratio of the pixel size to the pixel size of the image. Now for the data. This is a plot of s vs. r.

But that plot seems useless. Before making another plot, let’s combine the measurement from the images with the definition of angular size. If I plot s vs. 1/r, it should be a linear plot with a slope of L/FOV. Here is that plot.

Check that out. A nice straight line. The slope of the linear function fitting this data is 0.274 m (yes, the slope has units of meters). From this and the value of L (0.304 m), I can solve for FOV.

Just for fun, I can convert that FOV to degrees and I get 63.54° (the angular field of view for the iPhone 6). Awesome? Yes. Useful? Yes.